Question

What is the bulk modulus of oxygen if $32\text{g}$ of oxygen occupies $22.4\text{L}$ volume and the speed of sound in oxygen is $320\text{m/s}$ ?

• A. $2.5\times {10}^7\text{Pa}$
• B. $1.5\times {10}^5\text{Pa}$
• C. $3.5\times {10}^5\text{Pa}$
• D. $4.5\times {10}^5\text{Pa}$

Answer 1

The correct option is B $1.5\times {10}^5\text{Pa}$

Density of oxygen,
$\rho =\frac{m}{V}$
$\Rightarrow \rho =\frac{32\times {10}^{-3}}{22.4\times {10}^{-3}}=1.43{\text{kg/m}}^3$
We know that speed of sound wave is given by,
$v=\sqrt{\frac{B}{\rho }}$
$\Rightarrow B=v^2\rho$
$\Rightarrow B={320}^2\times 1.43=1.5\times {10}^5\text{Pa}$